Details

sample214.0ms

Algorithm

intervals

Results

80.0ms	1546×	body	80	nan
28.0ms	447×	body	80	valid
2.0ms	38×	body	80	overflowed
2.0ms	5×	body	640	valid
1.0ms	3×	body	320	valid
1.0ms	5×	body	160	valid

simplify40.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	31	10
1	62	10
2	137	10
3	344	10
4	1155	10
5	5001	10

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.3b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
0.1b	(* y (- (log z) t))
1.0b	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
4.9b	(log (- 1.0 z))

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

72×	`prod-diff`
66×	`add-sqr-sqrt`
65×	`*-un-lft-identity`
56×	`add-cube-cbrt`
53×	`distribute-rgt-in` `distribute-lft-in`
38×	`associate-+r+`
34×	`associate-+l+`
27×	`log-prod`
26×	`pow1`
22×	`associate--l+`
20×	`log-pow`
10×	`associate-*r/`
9×	`add-log-exp`
7×	`add-exp-log`
6×	`sub-neg` `flip3--` `associate-r` `add-cbrt-cube` `flip--`
5×	`distribute-lft-out--`
4×	`expm1-log1p-u` `frac-add` `log1p-expm1-u` `difference-of-squares`
3×	`exp-prod` `associate-l`
2×	`log-div` `sum-log` `rem-exp-log`
1×	`+-commutative` `fma-def` `flip3-+` `rem-log-exp` `exp-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 182

Calls

4 calls:

39.0ms	(exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
31.0ms	(* y (- (log z) t))
34.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
6.0ms	(log (- 1.0 z))

series406.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
65.0ms	(* y (- (log z) t))
171.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
41.0ms	(log (- 1.0 z))

simplify92.0ms

Algorithm

egg-herbie

Counts

194 → 194

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	904	1913
1	3501	1501
2	5001	1500

prune647.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.6b	(fma y (- (log z) t) (* (fma (* (cbrt (log (- 1.0 z))) (cbrt (log (- 1.0 z)))) (cbrt (log (- 1.0 z))) (- (* b 1))) a))
4.9b	(log (- 1.0 z))
4.9b	(log (- 1.0 z))
4.9b	(log (- 1.0 z))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

15×	`log-prod`
13×	`add-sqr-sqrt` `*-un-lft-identity`
7×	`pow1` `add-exp-log` `add-cube-cbrt`
6×	`log-div`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `rem-log-exp` `log-pow` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`fma-udef`

Counts

4 → 64

Calls

4 calls:

0.0ms	(fma y (- (log z) t) (* (fma (* (cbrt (log (- 1.0 z))) (cbrt (log (- 1.0 z)))) (cbrt (log (- 1.0 z))) (- (* b 1))) a))
6.0ms	(log (- 1.0 z))
6.0ms	(log (- 1.0 z))
6.0ms	(log (- 1.0 z))

series368.0ms

Counts

4 → 12

Calls

4 calls:

242.0ms	(fma y (- (log z) t) (* (fma (* (cbrt (log (- 1.0 z))) (cbrt (log (- 1.0 z)))) (cbrt (log (- 1.0 z))) (- (* b 1))) a))
40.0ms	(log (- 1.0 z))
45.0ms	(log (- 1.0 z))
41.0ms	(log (- 1.0 z))

simplify60.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 3 (54.0ms)

Iter	Nodes	Cost
0	224	569
1	619	499
2	2093	491
3	5002	484

prune476.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

4.9b	(log (- 1.0 z))
4.9b	(log (- 1.0 z))
4.9b	(log (- 1.0 z))
26.4b	(cbrt (pow (fma a (- (* (* (cbrt (log (- 1.0 z))) (cbrt (log (- 1.0 z)))) (cbrt (log (- 1.0 z)))) b) (* y (- (log z) t))) 3))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`log-prod`
12×	`cbrt-prod`
10×	`add-cube-cbrt`
7×	`pow1` `add-exp-log`
6×	`log-div`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`unpow-prod-down` `flip3--` `cube-prod` `rem-log-exp` `log-pow` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`cube-mult` `pow1/3` `unpow3` `rem-cbrt-cube` `sqr-pow`

Counts

4 → 77

Calls

4 calls:

6.0ms	(log (- 1.0 z))
6.0ms	(log (- 1.0 z))
9.0ms	(log (- 1.0 z))
2.0ms	(cbrt (pow (fma a (- (* (* (cbrt (log (- 1.0 z))) (cbrt (log (- 1.0 z)))) (cbrt (log (- 1.0 z)))) b) (* y (- (log z) t))) 3))

series309.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(log (- 1.0 z))
46.0ms	(log (- 1.0 z))
41.0ms	(log (- 1.0 z))
181.0ms	(cbrt (pow (fma a (- (* (* (cbrt (log (- 1.0 z))) (cbrt (log (- 1.0 z)))) (cbrt (log (- 1.0 z)))) b) (* y (- (log z) t))) 3))

simplify83.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 3 (73.0ms)

Iter	Nodes	Cost
0	273	974
1	815	927
2	2928	899
3	5001	890

prune547.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
0.1b	(exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
0.1b	(* y (- (log z) t))
1.0b	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

168×	`prod-diff`
155×	`*-un-lft-identity`
141×	`add-sqr-sqrt`
109×	`add-cube-cbrt`
108×	`distribute-rgt-in` `distribute-lft-in`
92×	`associate--l+`
74×	`associate-+r+`
46×	`pow1`
38×	`log-pow`
34×	`associate-+l+`
31×	`distribute-lft-out--`
24×	`log-prod`
14×	`difference-of-squares`
13×	`associate-r`
12×	`sub-neg` `associate-*r/`
9×	`add-log-exp`
8×	`add-exp-log` `add-cbrt-cube`
6×	`flip3--` `associate-l` `flip--`
4×	`expm1-log1p-u` `frac-add` `log1p-expm1-u`
3×	`exp-prod`
2×	`pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `rem-exp-log` `unswap-sqr`
1×	`+-commutative` `fma-def` `flip3-+` `exp-sum` `flip-+`

Counts

4 → 300

Calls

4 calls:

670.0ms	(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
164.0ms	(exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
27.0ms	(* y (- (log z) t))
246.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

series538.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
152.0ms	(exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
69.0ms	(* y (- (log z) t))
222.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

simplify151.0ms

Algorithm

egg-herbie

Counts

312 → 312

Iterations

Useful iterations: 2 (96.0ms)

Iter	Nodes	Cost
0	1091	5982
1	4469	4426
2	5001	4420

prune1.1s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes403.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	24
1	42	24
2	42	24

end0.0ms

sample5.9s

Algorithm

intervals

Results

2.3s	43625×	body	80	nan
778.0ms	13369×	body	80	valid
52.0ms	851×	body	80	overflowed
37.0ms	109×	body	640	valid
22.0ms	108×	body	320	valid
20.0ms	27×	body	1280	valid
16.0ms	128×	body	160	valid