Details

sample71.0ms

Algorithm

intervals

Results

20.0ms	236×	body	80	nan
19.0ms	256×	body	80	valid

simplify39.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune5.0ms

Filtered

1 candidates to 0 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 3.0b

Counts

2 → 1

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b	(* z (sqrt (+ t a)))
0.3b	(/ 2.0 (* t 3.0))
1.6b	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
6.1b	(/ (* z (sqrt (+ t a))) t)

rewrite1.0s

Algorithm

rewrite-expression-head

Rules

5600×	`frac-sub`
4092×	`add-sqr-sqrt`
3181×	`*-un-lft-identity`
2442×	`associate-/l*`
2267×	`add-cube-cbrt`
2241×	`associate-r`
2163×	`associate-/r*`
1900×	`frac-times`
1511×	`times-frac`
1468×	`flip3-+` `flip-+`
1365×	`prod-diff`
1354×	`associate-l`
1186×	`associate-*r/`
1051×	`flip3--` `flip--`
907×	`sqrt-prod`
658×	`unswap-sqr`
414×	`*-commutative`
328×	`associate--r+`
316×	`distribute-lft-out`
268×	`frac-2neg` `clear-num`
236×	`sqrt-div`
234×	`associate-/l/`
228×	`difference-of-squares`
169×	`distribute-lft-out--`
164×	`distribute-rgt-in` `distribute-lft-in`
55×	`fma-neg`
50×	`associate-*l/`
30×	`div-inv`
16×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `add-log-exp`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `associate--l+` `log1p-expm1-u`
3×	`sub-neg` `prod-exp` `cbrt-unprod`
2×	`+-commutative`
1×	`diff-log` `pow-prod-down`

Counts

4 → 4536

Calls

4 calls:

7.0ms	(* z (sqrt (+ t a)))
8.0ms	(/ 2.0 (* t 3.0))
277.0ms	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
12.0ms	(/ (* z (sqrt (+ t a))) t)

series351.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(* z (sqrt (+ t a)))
16.0ms	(/ 2.0 (* t 3.0))
182.0ms	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
86.0ms	(/ (* z (sqrt (+ t a))) t)

simplify2.5s

Algorithm

egg-herbie

Counts

4548 → 4548

Iterations

Useful iterations: 0 (152.0ms)

Iter	Nodes	Cost
0	9317	221969

prune26.5s

Filtered

4548 candidates to 3163 candidates (30.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	4545	3	4548
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	4546	3	4549

Merged error: 0.0b

Counts

4549 → 3

localize33.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt t)
0.6b	(cbrt t)
0.6b	(cbrt t)
1.1b	(fma (/ (* (cbrt z) (cbrt z)) (* (cbrt t) (cbrt t))) (/ (* (cbrt z) (sqrt (+ t a))) (cbrt t)) (- (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`fma-udef`

Counts

4 → 49

Calls

4 calls:

1.0ms	(cbrt t)
1.0ms	(cbrt t)
1.0ms	(cbrt t)
1.0ms	(fma (/ (* (cbrt z) (cbrt z)) (* (cbrt t) (cbrt t))) (/ (* (cbrt z) (sqrt (+ t a))) (cbrt t)) (- (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))))

series1.0s

Counts

4 → 12

Calls

4 calls:

187.0ms	(cbrt t)
183.0ms	(cbrt t)
183.0ms	(cbrt t)
466.0ms	(fma (/ (* (cbrt z) (cbrt z)) (* (cbrt t) (cbrt t))) (/ (* (cbrt z) (sqrt (+ t a))) (cbrt t)) (- (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))))

simplify66.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 3 (60.0ms)

Iter	Nodes	Cost
0	185	450
1	504	391
2	2161	378
3	5001	374

prune356.0ms

Filtered

61 candidates to 54 candidates (11.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	61	0	61
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	61	3	64

Merged error: 0.0b

Counts

64 → 3

localize43.0ms

Local error

Found 4 expressions with local error:

4.4b	(* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (/ (* t 3.0) (sqrt 2.0)))
5.8b	(- (* (/ (* z (sqrt (+ t a))) (* (cbrt t) (cbrt t))) (* (- a (/ 5.0 6.0)) (/ (* t 3.0) (sqrt 2.0)))) (* (cbrt t) (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (/ (* t 3.0) (sqrt 2.0))) (* (- a (/ 5.0 6.0)) (sqrt 2.0))))))
5.9b	(/ (* z (sqrt (+ t a))) (* (cbrt t) (cbrt t)))
22.1b	(/ (- (* (/ (* z (sqrt (+ t a))) (* (cbrt t) (cbrt t))) (* (- a (/ 5.0 6.0)) (/ (* t 3.0) (sqrt 2.0)))) (* (cbrt t) (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (/ (* t 3.0) (sqrt 2.0))) (* (- a (/ 5.0 6.0)) (sqrt 2.0)))))) (* (cbrt t) (* (- a (/ 5.0 6.0)) (/ (* t 3.0) (sqrt 2.0)))))

rewrite9.8m

Algorithm

rewrite-expression-head

Calls

4 calls:

115.0ms	(* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (/ (* t 3.0) (sqrt 2.0)))
1.1m	(- (* (/ (* z (sqrt (+ t a))) (* (cbrt t) (cbrt t))) (* (- a (/ 5.0 6.0)) (/ (* t 3.0) (sqrt 2.0)))) (* (cbrt t) (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (/ (* t 3.0) (sqrt 2.0))) (* (- a (/ 5.0 6.0)) (sqrt 2.0))))))
27.0ms	(/ (* z (sqrt (+ t a))) (* (cbrt t) (cbrt t)))
2.8m	(/ (- (* (/ (* z (sqrt (+ t a))) (* (cbrt t) (cbrt t))) (* (- a (/ 5.0 6.0)) (/ (* t 3.0) (sqrt 2.0)))) (* (cbrt t) (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (/ (* t 3.0) (sqrt 2.0))) (* (- a (/ 5.0 6.0)) (sqrt 2.0)))))) (* (cbrt t) (* (- a (/ 5.0 6.0)) (/ (* t 3.0) (sqrt 2.0)))))