Details

sample103.0ms

Algorithm

intervals

Results

40.0ms	735×	body	80	nan
10.0ms	189×	body	80	valid
8.0ms	26×	body	640	valid
5.0ms	6×	body	1280	valid
4.0ms	21×	body	320	valid
2.0ms	15×	body	160	valid

simplify69.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	27	9
1	57	8
2	136	8
3	312	8
4	709	8
5	1629	8
6	3564	8
7	5001	8

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 7.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- z 1.0) (log (- 1.0 y)))
0.0b	(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y)))) t)
0.2b	(* (- x 1.0) (log y))
5.2b	(log (- 1.0 y))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt`
32×	`*-un-lft-identity`
21×	`log-prod`
20×	`add-cube-cbrt`
11×	`pow1`
10×	`associate-l`
9×	`add-exp-log` `prod-diff` `add-log-exp`
8×	`distribute-rgt-in` `distribute-lft-in` `associate-r` `add-cbrt-cube`
6×	`distribute-lft-out--` `difference-of-squares`
4×	`expm1-log1p-u` `flip3--` `associate-*l/` `flip--` `log1p-expm1-u`
3×	`fma-neg` `log-pow`
2×	`log-div` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `rem-log-exp` `associate--l+` `sum-log`

Counts

4 → 114

Calls

4 calls:

14.0ms	(* (- z 1.0) (log (- 1.0 y)))
43.0ms	(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y)))) t)
11.0ms	(* (- x 1.0) (log y))
3.0ms	(log (- 1.0 y))

series292.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (- z 1.0) (log (- 1.0 y)))
152.0ms	(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y)))) t)
54.0ms	(* (- x 1.0) (log y))
44.0ms	(log (- 1.0 y))

simplify63.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	587	1089
1	2183	902
2	5001	886

prune387.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)
0.0b	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
0.0b	(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
0.2b	(* (- x 1.0) (log y))

rewrite126.0ms

Algorithm

rewrite-expression-head

Rules

63×	`add-sqr-sqrt`
60×	`*-un-lft-identity`
57×	`prod-diff`
51×	`add-cube-cbrt`
40×	`distribute-rgt-in` `distribute-lft-in`
34×	`associate-+r+`
28×	`flip3--` `flip--`
24×	`log-prod` `associate-*l/`
22×	`pow1`
16×	`frac-add`
14×	`log-pow`
13×	`associate--l+`
12×	`frac-times`
11×	`add-log-exp`
10×	`associate-r` `associate-l`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-+l+` `associate-*r/`
5×	`sub-neg` `distribute-lft-out--`
4×	`expm1-log1p-u` `log1p-expm1-u` `difference-of-squares`
3×	`fma-neg`
2×	`diff-log` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `fma-def` `flip3-+` `flip-+`

Counts

4 → 198

Calls

4 calls:

45.0ms	(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)
20.0ms	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
39.0ms	(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
11.0ms	(* (- x 1.0) (log y))

series509.0ms

Counts

4 → 12

Calls

4 calls:

241.0ms	(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)
146.0ms	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
64.0ms	(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
57.0ms	(* (- x 1.0) (log y))

simplify67.0ms

Algorithm

egg-herbie

Counts

210 → 210

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1127	4542
1	5001	3496

prune868.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.2b

localize37.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (fma (* (cbrt (log 1.0)) (cbrt (log 1.0))) (cbrt (log 1.0)) (- (* (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))) 1))) (- z 1.0))
0.2b	(fma (- x 1.0) (log y) (* (fma (* (cbrt (log 1.0)) (cbrt (log 1.0))) (cbrt (log 1.0)) (- (* (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))) 1))) (- z 1.0)))
0.5b	(* (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
59.2b	(fma (- (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (* (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

42×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
26×	`add-cube-cbrt`
21×	`pow1`
18×	`prod-diff` `sqrt-prod`
12×	`sqrt-div`
11×	`distribute-rgt-in` `distribute-lft-in` `associate-r`
9×	`associate-l`
8×	`add-exp-log` `sqrt-pow1` `pow1/2` `swap-sqr` `add-cbrt-cube`
6×	`flip3-+` `flip-+`
5×	`pow-prod-up` `unswap-sqr`
4×	`expm1-log1p-u` `frac-times` `associate-*r/` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
3×	`pow-sqr`
2×	`sub-neg` `associate-l/` `prod-exp` `-commutative` `cbrt-unprod` `fma-udef`
1×	`pow2` `flip3--` `pow-plus` `sqrt-unprod` `rem-square-sqrt` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 125

Calls

4 calls:

12.0ms	(* (fma (* (cbrt (log 1.0)) (cbrt (log 1.0))) (cbrt (log 1.0)) (- (* (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))) 1))) (- z 1.0))
0.0ms	(fma (- x 1.0) (log y) (* (fma (* (cbrt (log 1.0)) (cbrt (log 1.0))) (cbrt (log 1.0)) (- (* (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))) 1))) (- z 1.0)))
20.0ms	(* (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
0.0ms	(fma (- (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (* (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))

series1.3s

Counts

4 → 12

Calls

4 calls:

147.0ms	(* (fma (* (cbrt (log 1.0)) (cbrt (log 1.0))) (cbrt (log 1.0)) (- (* (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))) 1))) (- z 1.0))
257.0ms	(fma (- x 1.0) (log y) (* (fma (* (cbrt (log 1.0)) (cbrt (log 1.0))) (cbrt (log 1.0)) (- (* (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))) 1))) (- z 1.0)))
107.0ms	(* (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
830.0ms	(fma (- (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (* (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))

simplify97.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	504	3021
1	2321	2593
2	5001	2522

prune700.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.2b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (fma (* (cbrt (log 1.0)) (cbrt (log 1.0))) (cbrt (log 1.0)) (- (* (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))) 1))) (- z 1.0))
0.2b	(* (- x 1.0) (log y))
0.5b	(* (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
59.2b	(fma (- (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (* (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-sqr-sqrt`
34×	`*-un-lft-identity`
30×	`add-cube-cbrt`
24×	`pow1`
18×	`prod-diff` `sqrt-prod`
15×	`associate-r`
14×	`distribute-rgt-in` `distribute-lft-in` `associate-l`
12×	`sqrt-div`
10×	`add-exp-log` `add-cbrt-cube`
8×	`sqrt-pow1` `pow1/2` `swap-sqr`
6×	`log-prod` `flip3-+` `flip-+` `unswap-sqr`
5×	`pow-prod-down` `pow-prod-up`
4×	`expm1-log1p-u` `frac-times` `associate-r/` `associate-l/` `log1p-expm1-u` `add-log-exp`
3×	`prod-exp` `pow-sqr` `*-commutative` `cbrt-unprod`
2×	`sub-neg` `flip3--` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`pow2` `pow-plus` `sqrt-unprod` `rem-square-sqrt` `log-pow` `fma-udef`

Counts

4 → 146

Calls

4 calls:

12.0ms	(* (fma (* (cbrt (log 1.0)) (cbrt (log 1.0))) (cbrt (log 1.0)) (- (* (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))) 1))) (- z 1.0))
11.0ms	(* (- x 1.0) (log y))
22.0ms	(* (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
0.0ms	(fma (- (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (* (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))

series1.2s

Counts

4 → 12

Calls

4 calls:

150.0ms	(* (fma (* (cbrt (log 1.0)) (cbrt (log 1.0))) (cbrt (log 1.0)) (- (* (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))) 1))) (- z 1.0))
53.0ms	(* (- x 1.0) (log y))
122.0ms	(* (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
844.0ms	(fma (- (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (* (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))

simplify105.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 2 (80.0ms)

Iter	Nodes	Cost
0	614	2910
1	2811	2509
2	5001	2441

prune749.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.2b

regimes627.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	57
1	59	57
2	71	57
3	73	57
4	73	57

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.1s	23667×	body	80	nan
319.0ms	5917×	body	80	valid
236.0ms	768×	body	640	valid
151.0ms	250×	body	1280	valid
128.0ms	678×	body	320	valid
49.0ms	420×	body	160	valid