Details

sample74.0ms

Algorithm

intervals

Results

22.0ms	256×	body	80	valid
18.0ms	273×	body	80	nan

simplify39.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	50	17
1	108	17
2	389	17
3	1761	17
4	5002	17

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(* z (sqrt (+ t a)))
0.3b	(/ 2.0 (* t 3.0))
2.3b	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
7.2b	(/ (* z (sqrt (+ t a))) t)

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

75×	`*-un-lft-identity`
63×	`prod-diff`
62×	`associate--r+`
49×	`add-sqr-sqrt`
45×	`add-cube-cbrt`
36×	`times-frac`
31×	`distribute-rgt-in` `distribute-lft-in`
20×	`frac-sub`
16×	`add-exp-log` `add-cbrt-cube`
15×	`distribute-lft-out`
12×	`div-inv`
9×	`flip3--` `flip--`
8×	`frac-times` `associate-*r/`
7×	`fma-neg` `associate-r`
6×	`pow1` `add-log-exp`
5×	`flip3-+` `sqrt-prod` `flip-+`
4×	`cbrt-undiv` `expm1-log1p-u` `sqrt-div` `div-exp` `associate-/r` `log1p-expm1-u` `associate-/l`
3×	`sub-neg` `associate-l` `prod-exp` `cbrt-unprod`
2×	`frac-2neg` `associate-*l/` `associate--l+` `clear-num` `associate-/l/` `unswap-sqr`
1×	`diff-log` `pow-prod-down` `*-commutative`

Counts

4 → 179

Calls

4 calls:

12.0ms	(* z (sqrt (+ t a)))
3.0ms	(/ 2.0 (* t 3.0))
44.0ms	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
7.0ms	(/ (* z (sqrt (+ t a))) t)

series343.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(* z (sqrt (+ t a)))
16.0ms	(/ 2.0 (* t 3.0))
181.0ms	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
81.0ms	(/ (* z (sqrt (+ t a))) t)

simplify53.0ms

Algorithm

egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1377	2637
1	5001	2324

prune931.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.5b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))
0.2b	(* z (sqrt (+ t a)))
0.3b	(/ 2.0 (* t 3.0))
6.5b	(fma (* z (sqrt (+ t a))) (/ 1 t) (- (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))))

rewrite171.0ms

Algorithm

rewrite-expression-head

Rules

78×	`*-un-lft-identity`
56×	`prod-diff`
51×	`add-sqr-sqrt`
41×	`add-cube-cbrt`
31×	`distribute-rgt-in` `distribute-lft-in`
27×	`times-frac`
16×	`distribute-lft-out`
13×	`add-exp-log` `associate-r` `add-cbrt-cube`
9×	`div-inv`
8×	`pow1` `frac-times` `flip3--` `associate-l` `flip--`
6×	`associate-*r/` `frac-sub`
5×	`sqrt-prod`
4×	`expm1-log1p-u` `flip3-+` `flip-+` `log1p-expm1-u` `add-log-exp`
3×	`prod-exp` `cbrt-unprod` `associate-/l*` `distribute-lft-out--` `unswap-sqr`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `div-exp` `pow-prod-down` `associate-l/` `associate--l+` `-commutative` `difference-of-squares`
1×	`frac-2neg` `clear-num` `associate-/r*` `fma-udef`

Counts

4 → 161

Calls

4 calls:

148.0ms	(* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))
12.0ms	(* z (sqrt (+ t a)))
3.0ms	(/ 2.0 (* t 3.0))
0.0ms	(fma (* z (sqrt (+ t a))) (/ 1 t) (- (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))))

series339.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))
59.0ms	(* z (sqrt (+ t a)))
21.0ms	(/ 2.0 (* t 3.0))
197.0ms	(fma (* z (sqrt (+ t a))) (/ 1 t) (- (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))))

simplify105.0ms

Algorithm

egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 2 (83.0ms)

Iter	Nodes	Cost
0	900	2516
1	4225	1991
2	5001	1986

prune654.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.5b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt (+ t a)) t)
0.3b	(/ 2.0 (* t 3.0))
0.3b	(/ 2.0 (* t 3.0))
4.0b	(fma z (/ (sqrt (+ t a)) t) (- (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

32×	`*-un-lft-identity`
27×	`times-frac`
24×	`add-sqr-sqrt` `add-cube-cbrt`
16×	`add-exp-log` `sqrt-prod` `add-cbrt-cube`
13×	`associate-/l*`
5×	`cbrt-undiv` `div-exp` `associate-/r*`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `distribute-lft-out` `add-log-exp`
3×	`frac-2neg` `clear-num` `div-inv`
2×	`sqrt-div` `prod-exp` `cbrt-unprod` `associate-/l/`
1×	`flip3-+` `flip-+` `fma-udef`

Counts

4 → 103

Calls

4 calls:

8.0ms	(/ (sqrt (+ t a)) t)
3.0ms	(/ 2.0 (* t 3.0))
3.0ms	(/ 2.0 (* t 3.0))
0.0ms	(fma z (/ (sqrt (+ t a)) t) (- (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))))

series308.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(/ (sqrt (+ t a)) t)
16.0ms	(/ 2.0 (* t 3.0))
16.0ms	(/ 2.0 (* t 3.0))
213.0ms	(fma z (/ (sqrt (+ t a)) t) (- (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))))

simplify39.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	378	688
1	1172	613
2	5001	603

prune616.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.5b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ t a))
0.2b	(* z (sqrt (+ t a)))
0.8b	(fma a b (- (fma a c (* 0.8333333333333334 c))))
6.1b	(fma (* z (sqrt (+ t a))) (/ 1 t) (- (fma a b (- (fma a c (* 0.8333333333333334 c))))))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
9×	`sqrt-prod`
8×	`add-cube-cbrt`
7×	`pow1` `associate-r`
6×	`add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u` `add-log-exp`
3×	`associate-l`
2×	`flip3-+` `associate-*r/` `flip-+` `fma-udef` `distribute-lft-out` `unswap-sqr`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `hypot-def`

Counts

4 → 66

Calls

4 calls:

4.0ms	(sqrt (+ t a))
12.0ms	(* z (sqrt (+ t a)))
0.0ms	(fma a b (- (fma a c (* 0.8333333333333334 c))))
0.0ms	(fma (* z (sqrt (+ t a))) (/ 1 t) (- (fma a b (- (fma a c (* 0.8333333333333334 c))))))

series290.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(sqrt (+ t a))
64.0ms	(* z (sqrt (+ t a)))
35.0ms	(fma a b (- (fma a c (* 0.8333333333333334 c))))
157.0ms	(fma (* z (sqrt (+ t a))) (/ 1 t) (- (fma a b (- (fma a c (* 0.8333333333333334 c))))))

simplify44.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	348	482
1	1181	423
2	5001	410

prune365.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.5b

regimes470.0ms

Accuracy

53.4% (0.9b remaining)

Error of 1.3b against oracle of 0.4b and baseline of 2.4b

bsearch134.0ms

Steps

Iters	Range		Point
7	1.380535628283313e-236	2.623890731806373e-235	1.888010628839333e-236

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	63	46
1	65	46
2	65	46

end0.0ms

sample1.8s

Algorithm

intervals

Results

576.0ms	8000×	body	80	valid
543.0ms	7980×	body	80	nan